Related papers: On the Goodness-of-Fit Testing for Ergodic Diffusi…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
The supremum of the standardized empirical process is a promising statistic for testing whether the distribution function $F$ of i.i.d. real random variables is either equal to a given distribution function $F_0$ (hypothesis) or $F \ge F_0$…
Suppose that a sequence of data points follows a distribution of a certain parametric form, but that one or more of the underlying parameters may change over time. This paper addresses various natural questions in such a framework. We…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial data sets that are exchangeable with the real data under the null hypothesis (but not under the…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
A novel goodness-of-fit strategy is introduced for testing models of angular power spectra with unknown parameters. Using this strategy, it is possible to assess the validity of such models without specifying the distribution of the angular…
We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…
We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) -- inferred from noisy…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
The L\'evy distribution, alongside the Normal and Cauchy distributions, is one of the only three stable distributions whose density can be obtained in a closed form. However, there are only a few specific goodness-of-fit tests for the…
Various distribution free goodness-of-fit test procedures have been extracted from literature. We present two new binning free tests, the univariate three-region-test and the multivariate energy test. The power of the selected tests with…
In this review, the state-of-the-art for goodness-of-fit testing for spatial point processes is summarized. Test statistics based on classical functional summary statistics and recent contributions from topological data analysis are…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
The problem of making practical, useful goodness of fit tests in the Bayesian paradigm is largely open. We introduce a class of special cases (testing for uniformity: have the cards been shuffled enough; does my random generator work) and a…
Two new goodness of fit tests for the Pareto type-I distribution for complete and right censored data are proposed using fixed point characterization based on Steins type identity. The asymptotic distributions of the test statistics under…
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…
The objective of this text is to propose and study goodness-of-fit tests for DBP, which are consistent. Since the probability generating function (fgp) characterizes the distribution of a random vector and can be estimated consistently by…